Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate

Analytical features of the SIR model and their applications to COVID-19

“…The SARS-Cov-2 pandemic has introduced an evident research boom into biophysical and mathematical modeling of infection expansions. Main efforts have been related to identification of factors [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] that help prognosticate the pandemic development what is a clear concern in the atmosphere of anxiety and social limitations. Among a variety of infection expansion model types, the SIR- (susceptible-infectives-recovered, where infectives are indistinguishable from ill) models occupy a particular place.…”

Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation

“…Thus our paper focuses on a stochastic staged progression AIDS model with the corresponding staged treatment and second-order perturbation. In contrast, by means of the previous theory and existing method, like [23] , [25] , [30] , [31] , [33] , it is fifficult to obtain the suitable results of stationary distribution and extinction of more realistic stochastic system (2) . The main difficulties are described by Eliminating the influence of second-order perturbations.…”

“…In addition, various bio-mathematical models are inevitably affected by the environmental variations, see [17] . Consequently, some interesting stochastic epidemic models have been proposed and investigated in the past few decades [19] , [21] , [22] , [23] , [25] , [26] . Similarly, some authors also analyzed the corresponding stochastic HIV/AIDS models with various incidence rate types [24] , [27] , [28] .…”

Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

“…( [28] ) Let be a symmetric matrix, for the three-dimensional algebraic equation where If and then is positive definite, which follows …”

“…Moreover, the above random fluctuations are all assumed to be types of white noise. Therefore, many authors have formulated the relevant stochastic differential equations (SDEs) with linear noises for the transmission of various epidemics [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] . As an example, Qi and Jiang [29] studied the impact of virus carrier screening and actively seeking treatment on the dynamical behavior of a stochastic HIV/AIDS epidemic model with bilinear incidence.…”